Question: Which of the following numbers is a factor of 56? ${3,5,8,9,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $56$ by each of our answer choices. $56 \div 3 = 18\text{ R }2$ $56 \div 5 = 11\text{ R }1$ $56 \div 8 = 7$ $56 \div 9 = 6\text{ R }2$ $56 \div 13 = 4\text{ R }4$ The only answer choice that divides into $56$ with no remainder is $8$ $ 7$ $8$ $56$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $56$ $56 = 2\times2\times2\times7 8 = 2\times2\times2$ Therefore the only factor of $56$ out of our choices is $8$. We can say that $56$ is divisible by $8$.